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Learning Nonparametric Volterra Kernels with Gaussian Processes
Magnus Ross · Michael T Smith · Mauricio Álvarez

Wed Dec 08 12:30 AM -- 02:00 AM (PST) @

This paper introduces a method for the nonparametric Bayesian learning of nonlinear operators, through the use of the Volterra series with kernels represented using Gaussian processes (GPs), which we term the nonparametric Volterra kernels model (NVKM). When the input function to the operator is unobserved and has a GP prior, the NVKM constitutes a powerful method for both single and multiple output regression, and can be viewed as a nonlinear and nonparametric latent force model. When the input function is observed, the NVKM can be used to perform Bayesian system identification. We use recent advances in efficient sampling of explicit functions from GPs to map process realisations through the Volterra series without resorting to numerical integration, allowing scalability through doubly stochastic variational inference, and avoiding the need for Gaussian approximations of the output processes. We demonstrate the performance of the model for both multiple output regression and system identification using standard benchmarks.

Author Information

Magnus Ross (University of Sheffield)
Michael T Smith (University of Sheffield)

I’m currently a post-doc researcher at the University of Sheffield, in Neil Lawrence’s lab. We’re developing new tools to allow data to be anonymised, through the framework of differential privacy. As part of an innovate UK collaboration we’re building the scikic inference tool, which will provide both a conversation interface and a backend API for inferring demographic and lifestyle features about individuals. It is hoped it will be a useful tool to demonstrate the power of machine learning. In the future we hope to develop a user-centric data model for the analysis and storage of user data, with the motivation that personalised medicine and associated research requires access to user data. I spent most of 2014 lecturing at Makerere University, Kampala, Uganda. There I became involved in the field of Development Informatics, and have several on-going research topics; covering air pollution, nutrition-data, automated microscopy, traffic collision data and malaria distribution prediction. A variety of machine learning methods have been applied (for example Gaussian Process models for the model of malaria distribution). More details about some of these projects can be found at the Artificial Intelligence in the Developing World (AI-DEV) group’s website.

Mauricio Álvarez (University of Sheffield)

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